On the Resilience of Direction-Shift Keying Against Phase Noise and Short Channel Coherence Time at mmWave Frequencies

Short channel coherence time and oscillator phase noise are two major impairments in millimeter-wave (mmWave) communication systems. Several studies indicate that a substantial fraction of the available bandwidth may be required as overhead to compensate for these impairments, potentially exceeding one third of the total capacity. In this paper, we study Direction-Shift Keying (DSK), a variant of Spatial Modulation (SM), which encodes information in the Direction-of-Arrival (DoA) rather than in the signal amplitude or phase. DSK is implemented over a Distributed Antenna System (DAS), enabling angular resolvability of the transmitted signals. We first derive the structure of the optimal detector for a mobile device equipped with M antennas. We then introduce and characterize the Direction Coherence Time (DCT), defined as the temporal interval over which the DoA remains approximately invariant. Our analysis shows that DCT scales with d/v (transmitter-receiver distance over velocity), whereas the conventional Channel Coherence Time (CCT) scales with λ /v , revealing a coherence-time gain proportional to d/λ , which can exceed several orders of magnitude in mmWave systems. Furthermore, we show that the proposed detector inherently cancels receiver phase noise, eliminating the need for explicit phase-noise tracking. Simulation results validate the analytical findings and demonstrate the robustness of DSK in mobile mmWave environments in the presence of phase noise.